What is the purpose of the "Grid" object type?
I don't think there is any difference, other than it's slightly  faster to add a grid than to add a plane and subdivide.

From the wiki:


  A standard grid is made out of n by m vertices. The resolution of the
  x-axis and y-axis can be specified in the context panel in the Tool
  Shelf which appears when the object is created; the higher the
  resolution, the more vertices are created. Example objects that can be
  created out of grids include landscapes (with the proportional editing
  tool or Displace modifier) and other organic surfaces. You can also
  obtain a grid when you create a plane and then use a subdivide
  modifier in Edit mode.


emphasis mine